for any increasing, concave utility function *U*( ), where these expectations are “linear in the probabilities” as per VNM-expected utility theory.

If we further assume *U*( ) is homogeneous of degree *ν* and that the start-of-period wealth is *Y*_{0}, then

$\begin{array}{l}{Y}_{0}^{\nu}EU(1+{\tilde{r}}_{P*})>{Y}_{0}^{\nu}EU(1+{\tilde{r}}_{P})\hfill \\ EU({Y}_{0}(1+{\tilde{r}}_{P*}))>EU({Y}_{0}(1+{\tilde{r}}_{P}))\hfill \end{array}$ (6.9)

(6.9)

for any increasing, concave utility function *U*( ). If our investor’s utility function is increasing, concave, and homogeneous, his expected utility will thus increase with the inclusion of *A*.

Note that expectations in Eq. (6.9) are ...

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